Applying a texture to a cube shows up in the editor under the texture viewport and doesn't in render
So i had a look , but no textures were in the file so i took a guess , What i THINK is wrong is that you have assigned the material with no texture , To fix this , in the image below there are 2 materials , click the negative button ( make sure you have selected the material with no texture ) . Then go into edit mode , and press a until everything is selected , Click the logo material and click assign